Providing Justice for Asylum Seekers Act of 2019 This bill limits when an alien may be removed from the United States in absentia. To remove an alien in a proceeding without the alien present, the Department of Homeland Security (DHS) must establish that the alien (1) had sufficient written notice of the proceeding; (2) is removable; and (3) has a pattern of failing to report to DHS, if the alien was required to periodically report. Currently, DHS is not required to prove a pattern of failure to report. The bill also gives an immigration judge discretion as to whether to remove an alien in absentia after DHS has established its case. Currently, the judge must remove an alien after DHS has established its case. If an alien is ordered removed in absentia, a motion to reopen the case due to exceptional circumstances leading to the alien's failure to appear at the proceeding may be filed at any time, where currently such a motion must be filed within 180 days of the removal order. The bill also allows a motion to reopen to be filed at any time if the alien is a minor child. If there is a change in the time or place of any removal proceeding, and it is not practicable to provide written notice to the alien in person, DHS must notify the alien and the alien's counsel through the mail. Currently, DHS is only statutorily required to notify the alien or the alien's counsel through the mail.